nLab
coseparable coring

Coseparability of corings is a dual notion to separability of rings? (where one requires that the multiplication map is split).

An AA-coring(C,Δ,ϵ)(C,\Delta,\epsilon) is coseparable if the comultiplication Δ:C→C⊗AC\Delta:C\to C\otimes_A C splits as a CC-CC-bicomodule morphism. In other words, there is a morphism of AA-AA-bimodules p:C⊗AC→Cp: C\otimes_A C\to C such that